Question
The inverse of matrix
is
- A
The correct answer is: A
![vertical line A vertical line equals negative 1 left parenthesis 1 plus 0 right parenthesis equals negative 1](data:image/png;base64,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)
![a d j left parenthesis A right parenthesis equals open square brackets table row cell A subscript 11 end subscript end cell cell A subscript 21 end subscript end cell cell A subscript 31 end subscript end cell row cell A subscript 12 end subscript end cell cell A subscript 22 end subscript end cell cell A subscript 32 end subscript end cell row cell A subscript 13 end subscript end cell cell A subscript 23 end subscript end cell cell A subscript 33 end subscript end cell end table close square brackets](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAABJCAYAAACKCDxGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAApgpYK8gAABcNJREFUeNrtXVGEVUEYHisryZIkK4kkPa1lH5IkvfSQHlYv2YcksZIkiR6yVhJJD0kvPSXJslaSlVhZK+klK/vQQ/Sw0kMiycqV5TbjzLXnzp1zZs7MP3PmdL+PnzX3nDvf+f7vnuaee84XYwAVroBPo/gADjjN6y+vTeDTCD6AA7bxWuG1wGscfJLn09doa8oWj3hN8DrL62ECx9LvfHx62RdGd8EhXvPy7528vtR8HOBD11sYXUKsNz/w2p0bW+Z1oKZjAB8YPYgY07yuKWO3eV2s6RjAB0YnF+OAPDupOMrrZQ38wQdGDyLG24IvPaJ0l9H285ri9bHg/UyvU/LJj7/jtS8hPmK+48R8YHRHMSZ53S95fYbXCWXsqdyvaB7T69R8BAbkMmI5ET6dfwlWifnA6A5iDLPsmvDWkm3OlzS6TdwUXz4CrYT4iA/fT2LTwugOYszyOmnYZhevz5GM7stHrJmXEuGznWXX2c/B6M3/wtJOqCnDco2+NxFdRJ0JoA+M3sdGF1/u5qXZUzHJEMsuP07C6DA61Zn8lTRWiiZpwegwOgVeMftfJ2Ob5AjLfk2F0RtqdNONRjFvRLKZqw4+4kz+mtceYj4wOsRAbyEGgN5CDAC9hRgAegsxAPQWYgDoLcQA0FuIAaC3EAO9BSAGehsM4qmWOw773WHhHqyF0WF0Uozweu+x/zv5HimKgazDNPmQG/0Pyx6FKhsTRh31EGWMZQ/epiYGsg7T5UNqdPEk+YphbFQa3VeUt9LwqYiBrMO0+ZAaXRzAjGGbu7wuEYhy2XGNH0oMZC+mzaent2KJcZPXd7aRsaG7N1g84f2A1y+W3UM8Jw/gurLdtDIm7jU+QiCKyPN7k4jRkXWYPp+e3s5LA2+Tpp/VnFXF+CLLntQWfw9JQ7c126r7/+Y1SCDKoHyvooMyFZXRkXXYDD5dvZ2QxszjCesNmpnSnLkFRHzBLsPYOqEofxM4oyPrsBl8unq7KM+oeSxpli5fWW84zYC8uqIaVx1bJxSlbqMj67A5fLp6q14GFH+vKTuMMn3YzUH5QVGXIepY0dKlqigpLF0osxdtshAp+Zjmq5OPLnvRl09Xb38oLx7WmO8UyzLwVIhlz2OLsQX5vr6mqfvLaIjsxc7JpSgLkZqPzXyx+XROeqvEfLo0/8Zrs7IWn1N2GNes4/NNzOOBZkx3edFFlEvyveoweujsRcbKc02o+djMF5OPKXuxKp8ezW+x7NLegFyXP2NZ/kceW3h9Yhu/bI7JqyTfNGZ8oRlTfzByFaXOH4xCZy+ashCp+Zjmi8nHJnuxKh+t5jck0Sl5dv/Oei8Zist+z+WnStyzckx+Ajcr2+nGmNxnxEOUVG8BoJjHJguREqb5YvKxyV505WPs7Q5H0jtLziD/801dPvPYZiFSwTRfbD4CZdmLPnyC9FYsfe7xulqyzQXm9hP+XVYeQNlUo1fJQqQ6k5fNF5uPaQ3uy4e0t2ckwTVGfx9K3UuK0PNUyUKkgGm+2Hzy0GUv+vLBswYRxSi7nh/7P4BNKQcyP19R9qIvHxgdYqC3EANAbyEGgN5CDAC9hRgAegsxAPQWYgDoLcQA0FuIgd4CEAO9hRgAegsxeoGswzT5wOiEYiDrMF0+MDqRGMg6TJsPjE4kBrIO0+YDoxOIgazD9PnA6J5iIOuwGXxgdE8xkHXYDD4wuocYyDpsDh8Y3UOMUNmLuuxBaj5Vshdj8zFlL7rwgdEdxQiVvdg5E65W5B4qezE2H5v5XPjA6A5ihM5etMkepOQj0EqIj2m+qnxgdEcxQmYv2mQPUvMpyzKMzcc0nwsfGL0mMcry2U3Zg9QoyzKMzcc0nw8fGD0howuUZQ9SwybLMCYfm/lc+cDoiRndZs1MdSavkmXYityLFjEfGD1Bo+uyB6lRJcswBp8q87nwgdE1a8BQeYM22YtF2YOxj7UuPqbsRVs+2uP7BytaK4gGRzinAAACgXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5hPC9taT48bWk+ZDwvbWk+PG1pPmo8L21pPjxtbz4oPC9tbz48bWk+QTwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyIgc2VwYXJhdG9ycz0ifCI+PG10YWJsZT48bXRyPjxtdGQ+PG1zdWI+PG1pPkE8L21pPjxtbj4xMTwvbW4+PC9tc3ViPjwvbXRkPjxtdGQ+PG1zdWI+PG1pPkE8L21pPjxtbj4yMTwvbW4+PC9tc3ViPjwvbXRkPjxtdGQ+PG1zdWI+PG1pPkE8L21pPjxtbj4zMTwvbW4+PC9tc3ViPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bXN1Yj48bWk+QTwvbWk+PG1uPjEyPC9tbj48L21zdWI+PC9tdGQ+PG10ZD48bXN1Yj48bWk+QTwvbWk+PG1uPjIyPC9tbj48L21zdWI+PC9tdGQ+PG10ZD48bXN1Yj48bWk+QTwvbWk+PG1uPjMyPC9tbj48L21zdWI+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtc3ViPjxtaT5BPC9taT48bW4+MTM8L21uPjwvbXN1Yj48L210ZD48bXRkPjxtc3ViPjxtaT5BPC9taT48bW4+MjM8L21uPjwvbXN1Yj48L210ZD48bXRkPjxtc3ViPjxtaT5BPC9taT48bW4+MzM8L21uPjwvbXN1Yj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PC9tYXRoPlbtHfEAAAAASUVORK5CYII=)
![A subscript 11 end subscript equals 0 comma A subscript 12 end subscript equals negative 1 comma A subscript 13 end subscript equals 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAARCAYAAACLvqONAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAl5JREFUeNrtWj1IQzEQDqWIQxHEoRQRQUQ6ujpIcSkiIkUQcRARoYOTg5uIU3cREYqIg4MgTlKKICIiDoKUIk6Cg2MXR5EiPC+8K5SS99cmeZfoBx+01zZ93+XuJXd5jPlji9HGAPAI+IQso61bUNcrCxPAXWBdwljWxsgysAlMEhZ3C1xoez+Ptm5ggl5ZOAMWgU6P41gbI4PAF+ANsEBU2BLwQGDfB65EHMsEvSrQSwJYHSNl/MIa8JCouEtgXmCfwc+iwAS91BLA2hiZAlbwdRr4rmESgijCJ7BPYOe2RoT/N0UvpQSwNkb4Xu4ZONJmqwGzBLP7x+ezZsgxTNJLJQGsjpE94HaHrQTcNEzcd8gxTNKrYhXpJgGsjZEsZnIncsArgpPZ8Fje+kNugUzTS2EFsDpGHnwGF7W6gnrJMnvNXgXOrMCeD1kEy9Tb/rtH4LilWyBVPqt7FKvaYqSIrSEvnAPnOmxBvWRZvWYvLAKPBfZTFtwGVaGXI4FbgZqFCaDKZ62V5SOuGMkwt5+b8hlow0e8I/kuEwV3zD2JTOJStwO8F0wMv4aCJr1RahCqCaDbZwns2MQSIxfMPR3zwzDwjWAC8MOYEwy4L+b2plMBk6lab06QhCYU0XH5bIi55wjrMcaI0mXUITDhouVZhd4M1gBjzHzo8Fkr+VZNdhT1BJgEvjJ5z6s4PkV/BZPAdOjyGQd/MK2EtcJ/AigAX5rTivXyoK+y3p5EpQQdPjO1bjJyC6Rab5X9ndNjFTEyzdzTZeNE+RVScR7w6NZrm1adPuN3/mvgaBwX+Aux0DmJiUwiegAAAP90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+QTwvbWk+PG1uPjExPC9tbj48L21zdWI+PG1vPj08L21vPjxtbj4wPC9tbj48bW8+LDwvbW8+PG1zdWI+PG1pPkE8L21pPjxtbj4xMjwvbW4+PC9tc3ViPjxtbz49PC9tbz48bW8+LTwvbW8+PG1uPjE8L21uPjxtbz4sPC9tbz48bXN1Yj48bWk+QTwvbWk+PG1uPjEzPC9tbj48L21zdWI+PG1vPj08L21vPjxtbj4wPC9tbj48L21hdGg+cAl4hQAAAABJRU5ErkJggg==)
![A subscript 21 end subscript equals negative 1 comma A subscript 22 end subscript equals 0 comma A subscript 23 end subscript equals 0](data:image/png;base64,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)
, ![A subscript 32 end subscript equals 0 comma A subscript 33 end subscript equals negative 1](data:image/png;base64,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)
.
A real number multiplicative inverse is the number that, when multiplied by the original number, produces 1 (the identity). Because a× 1/a= 1 is the multiplicative inverse of a. When the inverse of a matrix is multiplied by a given matrix, it produces a multiplicative identity. For example, the inverse of a matrix A is A-1 and A.A-1=A-1.A=I, where I is the identity matrix.
A square matrix with one on the diagonal and zeros everywhere else is known as an identity matrix. Think of the identity matrix as the matrix's prime number.
An invertible matrix is one for which it is possible to calculate the inverse matrix and for which the determinant is not zero.