If A=[ 1 2 3 2 3 4 3 4 6 ] and B=[ -2 0 1

step 1 So in the given question we have two matrices that are being given as A is equal to 1, 2, 3, 2,

If A=[ 1 2 3 2 3 4 3 4 ...

If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 6\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}-2 & 0 & 1 \\ 0 & 3 & -2 \\ 1 & -2 & 1\end{array}\right]$, then $\mathrm{AB}$ is equal to
(a) I
(b) 6I
(c) 5I
(d) 2I

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Key Concepts

Scalar Multiplication

Scalar multiplication involves multiplying each entry of a matrix by a scalar (a constant number). This operation is used to scale matrices, and in the context of the problem, it helps in understanding how the product of two matrices can be expressed as a scalar multiple of the identity matrix, which simplifies the characterization of the matrix product.

Matrix Multiplication

Matrix multiplication is the process of taking the dot product of rows from the first matrix with columns of the second matrix to form a new matrix. This operation is fundamental in linear algebra and is used to combine linear transformations, solve systems of equations, and represent compositions of functions.

Identity Matrix

The identity matrix is a square matrix that has ones on the main diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix algebra, meaning that when any matrix is multiplied by the identity matrix (of compatible size), the original matrix is unchanged. It is a key concept in determining inverses and simplifying matrix expressions.

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